In the usual linear regression model we investigate the geometric structure of a class of minimax optimality criteria containing Elfving's minimax and Kiefer's $\phi_p$-criteria as special cases. It is shown that the optimal designs with respect to these criteria are also optimal for $A'\theta$, where $A$ is any inball vector (in an appropriate norm) of a generalized Elfving set. The results explain the particular role of the $A$- and $E$-optimality criterion and are applied for determining the optimal design with respect to Elfving's minimax criterion in polynomial regression up to degree 9.
@article{1176324453,
author = {Dette, H. and Heiligers, B. and Studden, W. J.},
title = {Minimax Designs in Linear Regression Models},
journal = {Ann. Statist.},
volume = {23},
number = {6},
year = {1995},
pages = { 30-40},
language = {en},
url = {http://dml.mathdoc.fr/item/1176324453}
}
Dette, H.; Heiligers, B.; Studden, W. J. Minimax Designs in Linear Regression Models. Ann. Statist., Tome 23 (1995) no. 6, pp. 30-40. http://gdmltest.u-ga.fr/item/1176324453/